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Positiveness of the Reproducing Kernel in the Space PD(R)

Published online by Cambridge University Press:  22 January 2016

Ivan J. Singer
Ivan J. Singer*
Affiliation:
Department of Mathematics, University of California
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An important problem in the study of the Hilbert space PD(R) of Dirichlet finite solutions of Δu = Pu on a Riemann surface R is to know the behavior of the reproducing kernel in PD(R). The main result of this paper is that the reproducing kernel is strictly positive.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 48 , December 1972 , pp. 67 - 72
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

[1] Nakai, M., The space of non-negative solutions of the equation Δ u= Pu on a Rie mann surface, Ködai Math. Sem. Rep. 12 (1960), 151–178.Google Scholar
[2] Nakai, M., The space of Dirichlet-ftnite solutions of the equation Δu = Pu on a Riemann surface, Nagoya Math. J. 18 (1961), 111–131.CrossRefGoogle Scholar
[3] Nakai, M., Dirichlet finite soltions of Δu = Pu, and classification of Riemann surfaces, Bull. Amer. Math. Soc. (3) 77 (1971), 381–385.Google Scholar
[4] Nakai, M., Dirichlet finite solutions of Δu = Pu on open Riemann surface, Ködai Math. Sem. Rep. (to appear).Google Scholar
[5] Nakai, M., The equation Δu—Pu on the unit disk with almost rotation free P ≥ 0, J. Diff. Eq. (to appear).Google Scholar
[6] Ozawa, M., Classification of Riemann surfaces, Ködai Math. Sem. Rep. 4 (1952), 63–76.Google Scholar
[7] Sario, L.—Nakai, M., Classification Theory of Riemann Surfaces Springer, 1970, 446 pp.Google Scholar